Method and apparatus for imaging the silhouette of an object occluding a light source using a synthetic aperature

ABSTRACT

A method of determining a silhouette of a remote object is disclosed herein. The method can include directing an array of telescopes at a star to sense an intensity of EM radiation over time and transmit signals corresponding to the intensity. The signals can be received at a computing device. Each signal can be indicative of a portion of an intensity diffraction pattern generated by an occlusion of the star by an occluding object. The signals can be combined to form a two-dimensional, intensity diffraction pattern. Each point on the intensity diffraction pattern associated with a time, a position of each telescope in the array, and an intensity of the sensed EM radiation. A silhouette of the occluding object can be determined based on the intensity diffraction pattern. A system for performing the method is also disclosed herein.

CROSS-REFERENCE TO RELATED APPLICATIONS

This continuation-in-part application claims the benefit of U.S.Provisional Patent Application Ser. No. 62/316,350 for a METHOD ANDAPPARATUS FOR IMAGING THE SILHOUETTE OF AN OBJECT OCCLUDING A LIGHTSOURCE USING A SYNTHETIC APERTURE, filed on Mar. 31, 2016, and U.S.Nonprovisional patent application Ser. No. 15/475,769 filed on Mar. 31,2017, both of which are hereby incorporated by reference in theirentirety.

BACKGROUND

1. Field

The present disclosure relates to novel data acquisition and imageprocessing.

2. Description of Related Prior Art

The problem of ground-based fine-resolution imaging of geosynchronoussatellites continues to be an important unsolved space-surveillanceproblem. If one wants to achieve 10 cm resolution at a range of 36,000km at λ=0.5 μm via conventional means, then a 180 m diameter telescopewith adaptive optics is needed (obviously prohibitively expensive).Disclosed is a passive-illumination approach that is radically differentfrom amplitude, intensity, or heterodyne interferometry approaches. Theapproach, called Synthetic-Aperture Silhouette Imaging (SASI), producesa fine-resolution silhouette image of the satellite.

A silhouette is the image of an object represented as a solid shape of asingle color (typically black) so that its edges match the object'soutline. Silhouettes arise in a variety of imaging scenarios. Theseinclude images of shadows that are cast either on a uniform or anon-uniform but known background. Silhouettes also occur when an opaqueobject occludes a known background. This case is particularly evidentwhen a bright background, such as the sun or the moon, is occluded by arelatively dark object, such as a satellite or an aircraft.

Various references reflect the state of the art in determining thesilhouette of an object including (1) R. G. Paxman, D. A. Carrara, P. D.Walker, and N. Davidenko, “Silhouette estimation,” JOSA A 31, 1636-1644(2014); (2) J. R. Fienup, R. G. Paxman, M. F. Reiley, and B. J. Thelen,“3-D imaging correlography and coherent image reconstruction,” inDigital Image Recovery and Synthesis IV, T. J. Schulz and P. S. Idell,eds., Proc. SPIE 3815-07 (1999); (3) R. G. Paxman, J. R. Fienup, M. J.Reiley, and B. J. Thelen, “Phase Retrieval with an Opacity Constraint inLAser IMaging (PROCLAIM),” in Signal Recovery and Synthesis, 1998Technical Digest Series 11, 34-36 (Optical Society of America,Washington D.C., 1998); and (4) R. G. Paxman, “Superresolution with anopacity constraint,” in Signal Recovery and Synthesis III, TechnicalDigest Series 15, (Optical Society of America, Washington D.C., 1989);

The background description provided herein is for the purpose ofgenerally presenting the context of the disclosure. Work of thepresently named inventors, to the extent it is described in thisbackground section, as well as aspects of the description that may nototherwise qualify as prior art at the time of filing, are neitherexpressly nor impliedly admitted as prior art against the presentdisclosure.

SUMMARY

A method of determining a silhouette of a remote object can includedirecting an array of telescopes at a star. Each telescope can beconfigured to sense an intensity of EM radiation over time and transmita time-dependent signal corresponding to the intensity. The method canalso include receiving, at a computing device having one or moreprocessors, the respective signals from each of the telescopes. Each ofthe signals can be indicative of a portion of an intensity diffractionpattern generated by an occlusion of the star over a period of time byan occluding object. The method can also include combining, with thecomputing device, the respective signals received from the telescopes toform a two-dimensional, intensity diffraction pattern. Each point on theintensity diffraction pattern can be associated with a time, a positionof each telescope in the array, and an intensity of the sensed EMradiation. The method can also include determining, with the computingdevice, a silhouette of the occluding object based on the intensitydiffraction pattern.

A system for determining a silhouette of a remote object includes anarray of telescopes and a computing device. The array of telescopes canbe configured to be directed at a star. Each telescope is configured tosense an intensity of EM radiation over time and transmit a signalcorresponding to the intensity. The computing device can have one ormore processors and can be configured to receive the respective signalsfrom each of the telescopes. Each of the signals can be indicative of aportion of an intensity diffraction pattern generated by an occlusion ofthe star over a period of time by an occluding object. The computingdevice can also be configured to combine the respective signals receivedfrom the telescopes to form a two dimensional, intensity diffractionpattern. Each point on the intensity diffraction pattern can beassociated with a time, a position of each telescope in the array, andan intensity of the sensed EM radiation. The computing device can alsobe configured to determine a silhouette of the occluding object based onthe intensity diffraction pattern.

BRIEF DESCRIPTION OF THE DRAWINGS

The detailed description set forth below references the followingdrawings:

FIG. 1 is a depiction of how a far-field shadow or diffraction patternis derived from an opaque object occluding light from a distant star;

FIG. 2 shows a moving intensity diffraction pattern that traverses anarray of telescopes;

FIG. 3 is a schematic and simplified flow diagram of a method applied inan exemplary embodiment of the present disclosure;

FIG. 4A is an image of a continuous silhouette;

FIG. 4B is an image of a discretized complement, treated as truth;

FIG. 4C is an image of a Fourier amplitude of FIG. 4B;

FIG. 4D is an image of an estimated object using phase retrieval;

FIG. 5A is a fine-resolution silhouette;

FIG. 5B is a noisy gray-scale image corresponding to FIG. 5A; and

FIG. 6 is a perspective view of an exemplary shadow track cast by thestar Zeta Ophiuchi and a representative satellite.

DETAILED DESCRIPTION

The present disclosure, as demonstrated by the exemplary embodimentsdescribed below, can provide a passive-illumination approach tofine-resolution imaging of geosynchronous satellites and other objects.SASI produces a fine-resolution silhouette image of a satellite. Whenplane-wave radiation emanating from a bright star is occluded by a GEOsatellite, then the light is diffracted and a moving diffraction pattern(shadow) is cast on the surface of the earth, as shown in FIG. 1. Theplane wave radiation prior to occlusion is referenced at 54. Theoccluding satellite is referenced at 56. The diffracted wave resultingfrom occlusion is referenced at 58. A far-field shadow, the intensitydiffraction pattern, is referenced at 16. The ground is referenced at 62and the height of the satellite 56 is referenced by Z. With priorknowledge of the satellite orbit and star location, the track of themoving shadow can be predicted with high precision. A linear array ofinexpensive hobby telescopes can be deployed roughly perpendicular tothe shadow track to collect a time history of the star intensity as theshadow passes by, as shown in FIG. 2. The array is referenced in FIG. 2at 8. The direction of travel on the ground of the moving shadow, orintensity diffraction pattern, relative to the stationary telescopearray is referenced at 64. According to Babinet's principle, the shadowis the complement of the diffraction pattern that would be sensed if theoccluding satellite were an aperture. If the satellite is small, thenthe Fraunhofer approximation is valid and the collected data can beconverted to the silhouette's Fourier magnitude. A method according tothe present disclosure also accommodates Fresnel diffraction in the caseof larger satellites or satellites closer to the ground. Aphase-retrieval algorithm, using the strong constraint that theocclusion of the satellite is a binary-valued silhouette (sometimescalled an opacity constraint), allows retrieval of the missing phaseleading to the reconstruction of a fine-resolution image of thesilhouette.

The inventor has perceived that silhouettes of satellites can be highlyinformative, providing diagnostic information about deployment ofantennas and solar panels, enabling satellite and antenna poseestimation, and revealing the presence and orientation of neighboringsatellites in rendezvous and proximity operations. However, the currentstate of the art is not capable of capturing such information. In oneembodiment of the present disclosure, a linear array of inexpensive(hobby) telescopes is placed on the ground in such a way that thediffraction pattern (or shadow) of the satellite, as the satelliteoccludes the star, passes perpendicular to the linear array. Eachtelescope tracks the star that will be occluded and has a field stop sothat light from other stars does not affect the signal. Each telescopethen collects a time-series signal of the occlusion. This can be donewith a single (non-imaging) high-temporal-bandwidth photodetector. Thetime series from all telescopes must be synchronized temporally so thata two dimensional measurement of the intensity diffraction pattern canbe constructed with temporal synthesis. The diffraction pattern can beused in conjunction with prior knowledge about a silhouette to retrievea fine-resolution image of the silhouette.

The prior knowledge used is that a silhouette is binary valued and thatit can be parameterized with a small number of parameters, relative to aconventional pixel parameterization. In the case of geosynchronoussatellites that are sufficiently small, the diffraction pattern willtend to be a Fraunhofer pattern that is closely related to the patternthat one would get if the two-dimensional occluding function were anaperture (the complement of the occlusion) by use of Babinet'sprinciple.

The intensity diffraction pattern is the magnitude squared of theFourier expression for the silhouette. Note thatatmospheric-turbulence-induced phase aberrations will have little or noeffect on the recorded intensity diffraction pattern, so long as thestar light is not refracted out of the field stop and light from otherstars is not refracted into the field stop. Accordingly, the opticaltolerances of the telescope can be relaxed.

The Fourier magnitude of the two-dimensional obscuration function isjust the square root of the intensity diffraction pattern.Phase-retrieval (PR) methods can be utilized to restore the silhouettefrom the Fourier magnitude. An elementary iterative-transform PRalgorithm is one approach.

Referring now to FIG. 3 an array 8 of telescopes, such as telescope 12can be directed at a source of light, such as a star. Each telescope caninclude a photodetector transducer configured emit a signalcorresponding to an intensity of sensed light, such as the signalreferenced at 20. As set forth above, each telescope can also include afield stop so that light from other stars does not affect the signalthat is emitted. All or less than all of the telescopes 12 can be hobbytelescopes.

The array 8 can be one-dimensional, as shown in FIG. 3. Theone-dimensional array 8 can be perpendicular to a path of movement ofthe shadow cast by an occluding object such as a satellite, the shadowdefining the intensity diffraction pattern. Alternatively, in one ormore embodiments of the present disclosure, the array 8 can betwo-dimensional.

The array 8 of telescopes 12 can be stationary or can be relocatable.For ease of relocation, the array can be mounted on a moveable platform.For example, the array 8 can be positioned on a series of rail cars, ontrucks, or on watercraft. The array 8 can be used to determine thesilhouettes of multiple, occluding objects. Alternatively, the array 8can used to determine the silhouette of a single object that occludesmultiple stars.

In one or more embodiments of the present disclosure, the sensed EMradiation can be allocated to a plurality of spectral bins by eachtelescope 12. Each of the spectral bins would correspond to one of aplurality of wavelength bands. The EM radiation can be partitioned byusing a dispersive element and a separate photodetector transducer foreach spectral bin. A dispersive element can be positioned in eachtelescope 12. Also, a respective field stop can be positioned in each ofthe telescopes 12 to limit sensed EM radiation to EM radiation emittedby a single source.

The signals from each telescope can be received at a computing devicehaving one or more processors. The computing device is representedschematically at 14. Each signal is indicative of an occlusion of thesource of light over a period of time by an occluding object, such as asatellite.

The computing device 14 can be configured to combine the respectivesignals received from the telescopes to form an intensity diffractionpattern having dimensions including time, a position of the telescope inthe array, and an intensity of the sensed EM radiation. Such a patternis referenced at 16. Portions or bands of the pattern 16 extending inthe horizontal direction and adjacent to one another along the verticalaxis correspond to the respective signals receiving from each telescope.Portions or bands of the pattern 16 extending in the vertical directionand adjacent to one another along the horizontal axis correspond to thevalue of each of the respective signals at a moment in time. Thecomputing device 14 can perform the operations illustrated within thedashed-line box 14 in FIG. 3 to reconstruct the discrete silhouettereferenced at 18 from the pattern 16.

In one embodiment of the present disclosure, the array 8 of telescopes12 is directed at a star as an object such as a satellite occludes thestar. Each telescope 12 is configured to sense an intensity of EMradiation that is emitted by the star over time and transmit a signalcorresponding to the intensity. The computing device 14 receives therespective signals from each of the telescopes 12. Each of the signalsis indicative of a portion of an intensity diffraction pattern generatedby the occlusion of the star by the occluding object. The computingdevice 14 combines the respective signals received from the telescopes12 to form a two-dimensional, intensity diffraction pattern. Theintensity diffraction pattern can be a Fresnel diffraction pattern or aFraunhoffer diffraction pattern.

The pattern 16 represents a two-dimensional, intensity diffractionpattern. Each point on the intensity diffraction pattern is associatedwith a time, a position of each telescope 12 in the array 8, and anintensity of the sensed EM radiation. Time is differentiated along thehorizontal direction of the pattern 16. The position of each telescope12 in the array 8 is differentiated along the vertical direction of thepattern 16. The intensity of the sensed EM radiation is differentiatedby relative darkness or brightness.

The computing device 14 can determine a silhouette of the occludingobject, such as referenced at 18, based on the intensity diffractionpattern. The computing device 14 can derive an initial estimatedcomplex-valued diffraction function in the data domain based on theintensity diffraction pattern. This is referenced at 22 in FIG. 3. Amagnitude and a phase of each pixel of the initial estimatedcomplex-valued diffraction function can be predetermined values or arandom set of values. In one exemplary approach, the magnitude of theinitial estimated complex-valued diffraction function can be deriveddirectly from the measured intensity diffraction pattern and thecorresponding phase can be randomly selected. The initial estimatedcomplex-valued diffraction function can be the starting point forretrieving, with the computing device 14, a final estimated set of phasevalues by iterative-transform phase retrieval.

The computing device 14 can convert the initial estimated complex-valueddiffraction function (or any subsequent then-current estimate of thecomplex-valued diffraction function) into an object-domainrepresentation by one of inverse Fresnel transform and inverse Fouriertransform. This is referenced at 24 in FIG. 3. The computing device 14can then impose a predetermined binary constraint on each of the set ofmagnitudes of the object domain representation of the initial estimatedcomplex-valued diffraction function (or the object domain representationof any subsequent then-current estimate of the complex-valueddiffraction function). This is referenced at 26 in FIG. 3. Thepredetermined binary constraint can be that the magnitude of each pixelwill be “1” (white) or “0” (black). In one exemplary approach,magnitudes of pixels of the object domain representation of the initialestimated complex-valued diffraction function (or the object domainrepresentation of any subsequent then-current estimate of thecomplex-valued diffraction function) that are greater than 0.5 can beassigned a value of “1” and pixels that are less than 0.5 can beassigned a value of “0.” The outcome of imposing the binary constraintis represented by f-hat, at 28.

The computing device 14 can next convert the initial or currentobject-domain representation (f-hat, at 28) into a subsequent estimateof the complex-valued diffraction function by one of forward Fresneltransform and forward Fourier transform. The conversion is referenced at30 and the output of the conversion is referenced at 32 in FIG. 3. Theoutput 32 is a complex-valued diffraction function, similar is nature tothe initial estimated complex-valued diffraction function considered at22.

The output 32 has a magnitude, the absolute value of F-hat. Thecomputing device 14 can replace the magnitude of the output 32 (thesubsequent estimate of the complex-valued diffraction function) with themagnitude of the initial estimated complex-valued diffraction function.The substitution operation is referenced at 34 and the output of theconversion is referenced at 36 in FIG. 3. The magnitude of the initialestimated complex-valued diffraction function can be the magnitudederived from the signals received by the telescopes. In such as anembodiment, the estimated portion of the initial estimatedcomplex-valued diffraction function is the phase.

The computing device 14 can evaluate an objective function thatquantifies the discrepancy between the current estimate and anacceptable solution. For example, the objective function can quantifythe difference between the object-domain representation f-hat-prime, at26, and that of f-hat, at 28. This discrepancy can be evaluated todetermine if the computing device 14 should perform further iterationsof the loop or cease silhouette-determining operations. Operations ceasewhen the silhouette 18 has been determined. As one alternative, theobjective function can quantify the difference between the data-domainrepresentation F-hat, at 32, and F-hat-prime, at 36.

The computing device 14 includes one or more processors. The one or moreprocessors can be configured to control operation of the computingdevice 14. It should be appreciated that the term “processor” as usedherein can refer to both a single processor and two or more processorsoperating in a parallel or distributed architecture. For example, afirst portion of the computing device 14 can be proximate to the array 8of telescopes 12. The first portion can be configured to directlyreceive the signals and to communicate the signals over a network. Asecond portion of the computing device 14 can be remote from the array 8of telescopes 12 and can be configured to receive the signals from thefirst portion over the network.

Embodiments of the present disclosure can apply compressive sensing (CS)to reduce the dimensions of the diffraction pattern detected by thearray of telescopes. The knowledge selected for application to reducedimensions is the object's orbit and opacity in transmission(binary-valued). The number of measurements is dramatically reducedbecause voluminous wavefront-sensing data are no longer needed andFourier phase information is not needed. In addition, the number andcost of sensing elements are dramatically reduced.

This embodiment disclosed herein is an unconventional method for imagingwithin a family of imaging modalities called “occlusion imaging.” Themethod can be practiced by hardware that is significantly less costlythan hardware applied in conventional ground-based imaging. For example,the exemplary embodiment can achieve 10 cm resolution for a silhouetteof a geosynchronous satellite; obtaining this degree of resolution usingconventional methods would require an aperture on the ground to beroughly 180 m in diameter (for A=0.5 mm), considering only diffractioneffects. This is over an order of magnitude larger than any telescope onthe earth today. In addition, it would take a Herculean effort toadaptively correct for turbulence-induced aberrations for such a largetelescope. Therefore, conventional ground-based imaging ofgeosynchronous satellites would be extremely expensive and eveninfeasible in the near term.

SASI produces a novel product, a fine-resolution silhouette, which canbe quite informative for identification, pose estimation, etc. SASIfundamentally leverages extremely powerful prior knowledge to produce aresult. The prior knowledge is that a silhouette is binary valued. Inaddition, silhouettes can be much more efficiently parameterized than byconventional pixel parameterization. These constraints are closelyrelated to an “opacity” constraint. Further, SASI is a type of passiveimaging, so it can collect silhouette images without being detected.SASI works even when the target (e.g. satellite or aircraft) doesn'tprovide a direct signal (such as when it is not illuminated by the sun).It is very difficult to construct counter measures for occlusionimaging.

In embodiments of the present disclosure, the optical tolerances of thetelescopes can be relaxed and therefore the telescopes can be lesscostly. Atmospheric turbulence has little effect on the detectedintensity diffraction pattern on the ground where the telescopes arepositioned. Respective field stops in each telescope can eliminatesignal contamination from light sources other than the occluded lightsource. Each telescope can function with a single non-imaging detector.

Silhouette estimation can involve an iterative-transform PR algorithm,as illustrated in FIG. 3. Alternatively silhouette estimation and phaseretrieval can involve nonlinear optimization of an objective function,such as a log-likelihood function. Gradients can be computed through theuse of algorithmic differentiation. Methods for global optimization canalso be developed.

One or more embodiments of the present disclosure can be generalized toaccommodate Fresnel diffraction which occurs when the occluding objectis closer to the earth or when the occluding object is larger in extent.Also, one or more embodiments of the present disclosure can achieveimproved signal-to-noise by using multiple spectral channels, by usingtelescopes with larger diameters, by using more telescopes (for exampleusing multiple linear arrays), and/or by using multiple stars andmultiple passes.

A variety of telescope-array geometries can be employed, including alinear array in which the diffraction pattern moves at any angle acrossthe linear array (the more off perpendicular, the finer the cross-motionsampling of the pattern), multiple parallel linear arrays, hexagonallydistributed arrays, or other spatially distributed array patterns.Additional noise immunity can be achieved by using efficientparameterizations, such as splines, instead of conventionalpixel-parameterization for the silhouette image.

A proof-of-concept simulation was performed to investigate the use ofthe opacity constraint in PR. A representative satellite silhouette wasdiscretized and its complement was taken to serve as the truth image.Using the complement simplified simulation but retained the essentialelements of a proof-of-concept evaluation. This image was then Fouriertransformed, yielding a complex-valued image. Only the amplitude portionof this image was saved and treated as preprocessed noiseless data. TheFourier amplitude was then used in a simple iterative PR algorithm, asillustrated in FIG. 3. The results, shown in FIGS. 4A through 4D, showthat the binary silhouette was retrieved perfectly. From FIGS. 4Athrough 4D it is clear that the opacity constraint works well for phaseretrieval. FIG. 4A is an image of a continuous silhouette. FIG. 4B isthe complement of a discretized version of 4A, treated as truth. FIG. 4Cis an image of the Fourier amplitude of FIG. 4B. Fourier amplitude datacan be estimated from the detected intensity diffraction pattern, inthis simulation a Fraunhofer diffraction pattern. FIG. 4D is an image ofan estimated object using the PR algorithm of FIG. 3.

The opacity constraint is potent and will be noise tolerant. This ispartly because a silhouette image is sparse relative to its gray-levelcounterpart. As an example, the fine-resolution silhouette shown in FIG.5A is efficiently characterized with spline parameters as opposed topixel values. A noisy gray-scale image corresponding to FIG. 5A is shownin FIG. 5B. The image of FIG. 5A is highly informative and complementsthe gray-scale image of FIG. 5B. Even though the silhouette of FIG. 5Ais highly articulated, the spline rendering represents a compressionfactor of 22.5 relative to its counterpart gray-level image. Clearly, itis easier to estimate fewer parameters in the presence of noise.

Another consideration for SASI is access to star shadows cast by a givenGEO satellite. This is a complicated problem that involves the satelliteorbit, the earth's rotation, the time of year, and selecting from a listof sufficiently bright stars. The inventor has learned how to map astar/satellite-shadow track on the earth's surface using AGI's STK. Anexample shadow track cast by the star Zeta Ophiuchi and arepresentative, occluding satellite is referenced at 38 in FIG. 6. Themoving shadow traverses this track (the semi-circle shown) in about 47minutes. The track cuts through the center of the CONUS, as well asportions of the Pacific and Atlantic oceans, all during the night. Notethat the track will change from day to day. The detail in FIG. 6 showsthe track for 10 consecutive days, which migrates roughly 1 mile inlatitude daily. These plots suggest a wide variety of geographic andtemporal choices for site selection, including the option for dailymonitoring of a high-interest satellite by using the same stars withonly modest relocation.

Fortunately, shadow tracks are precisely predictable for knownsatellites so that a relocatable observing system can be accuratelyprepositioned to capture the shadow signature. A collection plan for aspecific satellite can be formulated by evaluating candidate shadowtracks from differing stars on different days to find a region suitablefor deployment. Relocation could be achieved with rail cars (using aroughly north/south abandoned rail system), with a convoy of truckshaving telescopes mounted in the beds, or with a repurposed cargo shipfor ocean access. Note that the SASI signal will be relativelyinsensitive to ship motion.

Alternatively, telescopes can be deployed in a fixed (stationary)installation. In this case, daily tasking of the telescope array for agiven satellite can be planned by selecting from a catalog stars forwhich the star-satellite shadow tracks pass through the fixed array.

The telescopes in the SASI array can literally be hobby telescopes, eachwith a low-cost APD detector. The telescopes need to be deployed in alinear array that spans the desired effective diameter, say 180 m. Thelinear array provides a two-dimensional data set via temporal synthesis.The telescope/sensor modules are identical, enabling economies of scale.Each telescope tracks the designated star and collects its time historywith the aid of a field stop and a single APD detector. Signals must bedetected at kHz bandwidths and must be synchronized to millisecondaccuracy, which is easy to accommodate. The hardware described is simpleand inexpensive relative to other approaches. The expense foroperations, including possible relocation of the array, is manageable.

Because one or more embodiments of the present disclosure can collect anindirect signal provided by satellite occlusion, there is no limit tohow faint the satellite can be under direct observation. In fact, SASIworks well for unilluminated satellites (in the earth's shadow) orsatellites with low optical signature. Further, one or more embodimentsof the present disclosure can could be used to detect the silhouette ofasynchronous satellites (i.e. not geosynchronous) or even othernon-orbiting objects (e.g. aircraft). It is difficult to countermeasureocclusion.

SASI is insensitive to turbulence effects. SASI indirectly measuresFourier (or Fresnel) amplitude, which is insensitive toturbulence-induced aberrations, so long as the turbulence is near thepupil. This obviates the need for complicated phase-tracking andwavefront-sensing instrumentation.

Whereas other methods may need extended observation of a target to buildsufficient signal, the SASI acquisition is extremely quick. For onerepresentative geometry, the star shadow travels at a speed of 2.6km/sec. This means that the entire acquisition can take place in about1/10th of a second.

Multiple silhouettes can be collected from different aspects. Thesesilhouettes can then be used to construct a 3D visual hull of thesatellite. Silhouettes also complement gray-level images, providinginformation about regions of the satellite not illuminated.

The method can also be used when multiple stars appear in thefield-of-view of the system, such as in the case wherein binary stars orstar clusters, for which multiple stars are closely spaced in angle, areused. In this case, the satellite will occlude multiple stars andmultiple intensity diffraction patterns will be detected by the SASIsystem. For a given wavelength, the multiple intensity diffractionpatterns will have the same pattern but will be shifted with a knownshift corresponding to the angular position of the multiple stars. Theseshifted intensity diffraction patterns will be overlaid when detected.The detected signal of overlaid patterns can be used to estimate thesatellite silhouette.

While the present disclosure has been described with reference to anexemplary embodiment, it will be understood by those skilled in the artthat various changes may be made and equivalents may be substituted forelements thereof without departing from the scope of the presentdisclosure. In addition, many modifications may be made to adapt aparticular situation or material to the teachings of the presentdisclosure without departing from the essential scope thereof.Therefore, it is intended that the present disclosure not be limited tothe particular embodiment disclosed as the best mode contemplated forcarrying out this present disclosure, but that the present disclosurewill include all embodiments falling within the scope of the appendedclaims. The right to claim elements and/or sub-combinations that aredisclosed herein as other present disclosures in other patent documentsis hereby unconditionally reserved.

What is claimed is:
 1. A method of determining a silhouette of a remoteobject comprising: directing an array of telescopes at a star whereineach telescope is configured to sense an intensity of EM radiation overtime and transmit a signal corresponding to the intensity; receiving, ata computing device having one or more processors, the respective signalsfrom each of the telescopes, each of the signals indicative of a portionof an intensity diffraction pattern generated by an occlusion of thestar over a period of time by an occluding object; combining, with thecomputing device, the respective signals received from the telescopes toform a two-dimensional, intensity diffraction pattern with each point onthe intensity diffraction pattern associated with a time, a position ofeach telescope in the array, and an intensity of the sensed EMradiation; and determining, with the computing device, a silhouette ofthe occluding object based on the intensity diffraction pattern.
 2. Themethod of claim 1 wherein the intensity diffraction pattern is a Fresneldiffraction pattern.
 3. The method of claim 1 wherein the intensitydiffraction pattern is a Fraunhoffer diffraction pattern.
 4. The methodof claim 1 wherein at least some of the telescopes are hobby telescopes.5. The method of claim 4 wherein all of the telescopes are hobbytelescopes.
 6. The method of claim 1 further comprising: deriving, withthe computing device, an initial estimated complex-valued diffractionfunction in the data domain based on the intensity diffraction pattern,wherein a magnitude and a phase of each pixel of the initial estimatedcomplex-valued diffraction function are each of one of a predeterminedand a random set of values.
 7. The method of claim 6 wherein saiddetermining further comprises: retrieving, with the computing device, afinal estimated set of phase values by nonlinear-optimization-basediterative phase retrieval beginning with the initial estimatedcomplex-valued diffraction function.
 8. The method of claim 6 whereinsaid determining further comprises: retrieving, with the computingdevice, a final estimated set of phase values by iterative-transformphase retrieval beginning with the initial estimated complex-valueddiffraction function.
 9. The method of claim 8 wherein said determiningfurther comprises: converting, with the computing device, a currentestimate of the complex-valued diffraction function into anobject-domain representation by one of inverse Fresnel transform andinverse Fourier transform; and imposing, with the computing device, apredetermined binary constraint on each of the set of magnitudes of theobject domain representation of the current estimate of thecomplex-valued diffraction function.
 10. The method of claim 9 whereinsaid determining further comprises: converting, with the computingdevice after said imposing, a current object-domain representation intoa subsequent estimate of the complex-valued diffraction function by oneof forward Fresnel transform and forward Fourier transform; andreplacing, with the computing device, the magnitude of the subsequentestimate of the complex-valued diffraction function with the magnitudeof the initial estimated complex-valued diffraction function.
 11. Themethod of claim 10 wherein the predetermined binary constraint isfurther defined as being one of two alternative values, wherein saidimposing is further defined as replacing each value in the set ofmagnitudes of the object-domain representation with one of the twoalternative values.
 12. The method of claim 8 wherein said determiningfurther comprises: evaluating, with the computing device, an objectivefunction that quantifies a discrepancy between current values ofmagnitude during the iterative-transform phase retrieval and apredetermined value.
 13. The method of claim 12 wherein the discrepancyis further defined as between the set of magnitudes of a currentobject-domain representation and a predetermined binary constraint. 14.The method of claim 12 wherein the discrepancy is further defined asbetween the set of magnitudes of a current complex-valued diffractionfunction with the magnitude of the initial estimated complex-valueddiffraction function.
 15. The method of claim 1 further comprising:allocating the sensed EM radiation to a plurality of spectral bins eachcorresponding to one of a plurality of wavelengths; and partitioning theEM radiation by using a dispersive element and a separate photodetectortransducer for each spectral bin.
 16. The method of claim 1 furthercomprising: positioning a respective field stop in each of thetelescopes to limit sensed EM radiation to EM radiation emitted by thesource.
 17. The method of claim 1 wherein said directing comprises:directing a one-dimensional array of telescopes at the star wherein eachtelescope includes a photodetector transducer configured to detect thesignal corresponding to the intensity of the sensed EM radiation. 18.The method of claim 17 further comprising: arranging the one-dimensionalarray of telescopes to be approximately perpendicular to a path ofmovement of the intensity diffraction pattern.
 19. The method of claim 1wherein said directing further comprises: directing a two-dimensionalarray of telescopes at the source.
 20. The method of claim 1 furthercomprising: positioning the array of telescopes on a moveable platform.21. The method of claim 1 wherein the occluding object is a satelliteorbiting the Earth.
 22. The method of claim 1 further comprising:directing the array of telescopes at a second star wherein eachtelescope is configured to sense an intensity of EM radiation over timeand transmit a signal corresponding to the intensity of the second star;receiving, at the computing device, the respective signals associatedwith the second star from each of the telescopes, each of the signalsassociated with the second star indicative of a portion of an intensitydiffraction pattern associated with the second star generated by anocclusion of the second star over a period of time by an occludingobject; combining, with the computing device, the respective signalsassociated with the second star received from the telescopes to form atwo-dimensional, intensity diffraction pattern associated with thesecond star with each point on the intensity diffraction patternassociated with the second star defined by a time, a position of eachtelescope in the array, and an intensity of the sensed EM radiation; anddetermining, with the computing device, a silhouette of the occludingobject based on the intensity diffraction pattern associated with thestar and on the intensity diffraction pattern associated with the secondstar.
 23. A system for determining a silhouette of a remote objectcomprising: an array of telescopes configured to be directed at a starwherein each telescope is configured to sense an intensity of EMradiation over time and transmit a signal corresponding to theintensity; and a computing device having one or more processors andconfigured to receive the respective signals from each of thetelescopes, each of the signals indicative of a portion of an intensitydiffraction pattern generated by an occlusion of the star over a periodof time by an occluding object, said computing device also configured tocombine the respective signals received from the telescopes to form atwo dimensional, initial intensity diffraction pattern with each pointon the initial intensity diffraction pattern associated with a time, aposition of each telescope in the array, and an intensity of the sensedEM radiation, and said computing device also configured to determine asilhouette of the occluding object based on the intensity diffractionpattern.
 24. The system of claim 23 wherein said computing devicefurther comprises: a first portion being proximate to said array oftelescopes and configured to directly receive the signals and tocommunicate the signals over a network; and a second portion beingremote from said array of telescopes and configured to receive thesignals from said first portion over the network.
 25. The system ofclaim 24 wherein: said array comprises a plurality of telescopesarranged in at least one row; and said computing device is furtherdefined as configured to reconstruct the silhouette of the occludingobject from the sensed intensity of the EM radiation over time throughthe use of a phase-retrieval algorithm in the form of anonlinear-optimization-based phase retrieval.